Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice

Area of Science:

• Condensed Matter Physics
• Quantum Simulation
• Computational Physics

Background:

• Ultracold-atom simulations offer insights into the Hubbard model's charge and spin correlations.
• Numerical simulations of the Hubbard model, especially out of equilibrium, present significant computational challenges.

Purpose of the Study:

• To develop and benchmark novel discrete-time quantum Monte Carlo (QMC) methods for the square-lattice Hubbard model.
• To enable efficient numerical studies of both equilibrium and non-equilibrium properties of strongly correlated electron systems.

Main Methods:

• Devised and implemented two discrete-time QMC methods: fermionic-propagator QMC (FPQMC) and alternating-basis QMC (ABQMC).
• FPQMC uses real-space snapshots, while ABQMC alternates between real and reciprocal space snapshots.
• Both methods utilize matrices dependent on the number of particles, enabling computationally inexpensive updates.

Main Results:

• FPQMC demonstrates an excellent average sign in equilibrium, providing accurate results even with coarse imaginary-time discretization.
• ABQMC exhibits a worse average sign but still yields good results, and crucially, its sign problem is not time-dependent.
• ABQMC was successfully used to compute survival probabilities for experimentally relevant pure states out of equilibrium.

Conclusions:

• The developed FPQMC and ABQMC methods offer efficient tools for simulating the Hubbard model.
• ABQMC is particularly advantageous for studying non-equilibrium phenomena due to its time-independent sign problem.
• These methods open new avenues for investigating complex quantum phenomena in condensed matter systems.